Large Deformations of Giant Floppy Vesicles in Shear Flow

Abstract

The flow deformation and rheology of vesicles of a soluble surfactant are studied. Direct observation under shear flow reveals that the vesicles become strongly elongated to form an entangled structure of connected bilayer tubes. The large deformation is due to the permeability of the membrane and the large solubility of the surfactant. The formation of the entangled structure is observed in the rheology as a strong increase of the viscosity with time. [S0031-9007(98)07534-6] PACS numbers: 87.45.FtVesicles are closed membranes consisting of surfactant bilayers and have been intensively studied as model systems for biological cells [1]. More recently, the problem of the deformation of vesicles in hydrodynamic flows has been considered [2][3][4][5][6]. From a fundamental point of view, this is an interesting problem since both the surface area of the vesicle and its interior volume are usually supposed to be fixed [5,6]: The response to flow is then attributed to a dynamic surface tension. There is also a biological motive for understanding vesicle deformation in flow. One example is that of red blood cells, which are also vesicular structures. These have the capacity to pass through capillaries that are smaller than their own diameter, due to the deformation they undergo in the flow [7].The flexibility or "floppiness" of vesicles at rest is determined by their bending rigidity k, through the persistence length j of the membrane: j a exp͑2pk͞k B T͒, with a a molecular length, k B Boltzmann's constant, and T temperature [8]. If k ¿ k B T , j is large and the vesicle remains flat over large distances in the presence of thermal fluctuations. If k ø k B T , thermal fluctuations dominate, and the vesicle will appear very "floppy."In a dynamical situation, for instance, under flow, if the total volume within the vesicle does not change, conservation of the number of surfactant molecules in the membrane (conserved surface area) leads to a dynamic "effective" surface tension s e , which also contributes to the response of a vesicle in a flow field [5,6].Model vesicles are usually prepared from phospholipids, practically insoluble surfactants. A recent detailed study of the flow deformation shows that it is in general very small, and that even for high shear rates ͑ഠ18 s 21 ͒, the ratio of long and short axes of the vesicles L͞S ഠ 1.3: No large deformations are observed [4]. The deformation could be well described using the fixed area and volume constraints, allowing for evaluation of k and s e [4]. The two constraints thus lead to small deformations [4-6], accompanied by a "tank treading" motion, in which the membrane revolves around the vesicle interior [3,4].In this Letter we report extremely large deformations ͑L͞S ¿ 100͒ for vesicles that form spontaneously [9] in solutions of a soluble surfactant, even for very weak shear ͑ഠ0.5 s 21 ͒. Moreover, k for these vesicles is similar to that of phospholipid vesicles [4]: both are on the order of a few k B T . The large deformation entails the formation of very long and thin,...

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